Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x-5}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{5x^3-22x^2-17x+11}{x-5}=$
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} 5x^2+\phantom{1}3x-\phantom{1}2 \\ x-5|\overline{5x^3-22x^2-17x+11} \\ \mathllap{-(}\underline{5x^3-25x^2\phantom{-17x+11}\rlap )} \\ 3x^2-17x+11 \\ \mathllap{-(}\underline{3x^2-15x\phantom{+11}\rlap )} \\ -2x+11 \\ \mathllap{-(}\underline{-2x+10\rlap )} \\ 1 \end{array}$ We found that the quotient is $5x^2+3x-2$ and the remainder is $1$ : $\dfrac{5x^3-22x^2-17x+10}{x-5}=5x^2+3x-2+\dfrac{1}{x-5}$